The union, which balloted approximately 25,500 eligible members in England and Wales, said that based on its own surveys many members had had trouble receiving their ballot papers. The postal system in Britain has recently been disrupted by strikes.
"We have to conclude that our democratic process has been compromised by factors outside of our control," NAHT general secretary, Paul Whiteman, said in a statement.
"There has been a very strong appetite for action from those we have heard from, with a higher percentage voting 'Yes' to both strike and action short of strike than in our consultative online ballot."
A separate ballot in Wales met the threshold for strike action, the union said, without setting out dates for industrial action. In Northern Ireland school leaders have been engaged in action short of strike since Oct. 18 last year.
The union's chief said if its members felt that they had not had the chance to be heard "it may be that we have no option but to start again".
"The National Executive Committee will meet this week to establish our next steps," the union added.
(Reporting by Farouq Suleiman, Editing by Alistair Smout and William James)
